Problem: $\begin{aligned} &f(x)=3\cdot\sqrt{3x+10}+2 \\\\ &g(x)=x^2-7x \end{aligned}$ $(f\circ g) (10)=$
Answer: Let's start by rewriting $(f\circ g) (10)$ as $f(g(10))$. When evaluating composite functions, we work our way inside out. To evaluate $f(g(10))$, let's first evaluate $g(10)$. Then we'll plug that result into $f$ to find our answer. Let's evaluate $g({10})$. $\begin{aligned}g(x)&=x^2-7x\\\\ g({10})&=({10})^2-7({10})~~~~~~~~~~\text{Plug in }x={10}\\\\ &=100-70\\\\ &={30}\end{aligned}$ We now know that $f(g({10}))$ is the same as $f({30})$ because $g({10}) = {30}$. Let's evaluate $f({30})$. $\begin{aligned}f(x)&=3\cdot\sqrt{3x+10}+2\\\\ f({{30}})&=3\cdot\sqrt{3({30})+10}+2~~~~~~~~~~\text{Plug in }x={30}\\\\ &=3\cdot \sqrt{100}+2\\\\ &=32\end{aligned}$ The answer: $(f\circ g)(10) =32$